$\frac{1}{6}$ + $\frac{1}{12}$ + $\frac{1}{20}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$
= ($\frac{1}{6}$ + $\frac{1}{12}$) + ($\frac{1}{20}$ + $\frac{1}{30}$) + ($\frac{1}{42}$ + $\frac{1}{56}$)
= ($\frac{2}{12}$ + $\frac{1}{12}$) + ($\frac{1}{20}$ + $\frac{1}{30}$) + ($\frac{1}{42}$ + $\frac{1}{56}$)
= $\frac{1}{4}$ + $\frac{1}{20}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$
= ($\frac{1}{4}$ + $\frac{1}{20}$) + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$
= $\frac{3}{10}$ + $\frac{1}{30}$ + $\frac{1}{42}$ + $\frac{1}{56}$
= ($\frac{3}{10}$ + $\frac{1}{30}$) + $\frac{1}{42}$ + $\frac{1}{56}$
= $\frac{1}{3}$ + $\frac{1}{42}$ + $\frac{1}{56}$
= ($\frac{1}{3}$ + $\frac{1}{42}$) + $\frac{1}{56}$
= $\frac{5}{14}$ + $\frac{1}{56}$
= $\frac{20}{56}$ + $\frac{1}{56}$
= $\frac{21}{56}$
= $\frac{3}{8}$
